Massive spinning particle on anti-de Sitter space

TL;DR

This paper introduces an exactly solvable classical model for a massive spinning particle in anti-de Sitter space, linking energy minima to quantum spin conditions and generalizing to higher dimensions.

Contribution

It proposes a new point-particle model with gauge symmetries for describing massive spinning particles in AdS space, establishing classical-quantum spin relations and extending to arbitrary dimensions.

Findings

Model is exactly solvable.

Energy minimum condition relates to quantum spin.

Generalization to higher-dimensional AdS spaces is straightforward.

Abstract

To describe a massive particle with fixed, but arbitrary, spin on $d=4$ anti-de Sitter space $M^4$, we propose the point-particle model with configuration space ${\cal M}^6 = M^{4}\times S^{2}$, where the sphere $S^2$ corresponds to the spin degrees of freedom. The model possesses two gauge symmetries expressing strong conservation of the phase-space counterparts of the second- and fourth-order Casimir operators for $so(3,2)$. We prove that the requirement of energy to have a global positive minimum $E_o$ over the configuration space is equivalent to the relation $E_o > s$, $s$ being the particle's spin, what presents the classical counterpart of the quantum massive condition. States with the minimal energy are studied in detail. The model is shown to be exactly solvable. It can be straightforwardly generalized to describe a spinning particle on $d$-dimensional anti-de Sitter space $M^d$, with ${\cal M}^{2(d-1)} = M^d \times S^{(d-2)}$ the corresponding configuration space.